Born approximation for scattering of wave packets on atoms. I. Theoretical background for scattering of a wave packet on a potential field

摘要

Laser photons carrying non-zero orbital angular momentum are known andexploited during the last twenty years. Recently it has been demonstratedexperimentally that such (twisted) electrons can be produced and even focusedto a subnanometer scale. Thus, twisted electrons emerge as a new tool in atomicphysics. The state of a twisted electron can be considered as a specific wavepacket of plane waves. In the present paper-I we consider elastic scattering ofthe wave packets of fast non-relativistic particles on a potential field. Weobtain simple and convenient formulae for a number of events in such ascattering. The equations derived represent, in fact, generalization of thewell-known Born approximation for the case when finite sizes and inhomogeneityof the initial packet should be taken into account. To illustrate the obtainedresults, we consider two simple models corresponding to scattering of aGaussian wave packet on the Gaussian potential and on the hydrogen atom. Thescattering of twisted electrons on atoms will be considered in the nextpaper-II.